This paper proposes a strategy for coupling a Finite-Element description of structures with a Finite-Volume description of fluids by means of the Lagrange multipliers method, for the numerical simulation of Fluid-Structure Interaction problems in fast transient dynamics. The structural domain uses the classical explicit Central Difference time integration scheme, while in the fluid domain a node-centered Finite Volume scheme is adopted, which achieves second-order accuracy in space and in time by a predictor-corrector algorithm combined with a MUSCL-like technique. The FV time marching scheme is suitably adapted to enable ¿strong¿ coupling with the CD scheme via Lagrange multipliers. Numerical examples illustrate the effectiveness of the proposed procedure.